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Smooth economic analysis for general spaces of commodities

  • Accinelli, Elvio
  • Covarrubias, Enrique

This paper provides an extended framework to study general equilibrium theory with commodity spaces possibly of infinite dimensions. Our approach overcomes some difficulties found in the literature since it allows the study of the equilibrium when consumption sets may have an empty interior. It also overcomes the need for separable utilities or utilities that satisfy quadratic concavity. The results are based on restricting the mathematical notions of open neighborhoods, continuity, and derivatives at a point, to only those directions that lie within the positive cone. We prove in this setting ``directional'' equivalents of the Sard-Smale and Preimage Theorems. With these tools, we define the social equilibrium set and show that it is a directional Banach manifold. Together with a suitable definition of projection map, this framework allows a natural equivalent to infinite dimensions of the ``catastrophic'' approach to general economic equilibrium.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 53222.

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Date of creation: Jan 2014
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Handle: RePEc:pra:mprapa:53222
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  1. Yves Balasko, 1995. "Equilibrium Analysis of the Infinite Horizon Model with Smooth Discounted Utility Functions," Research Papers by the Institute of Economics and Econometrics, Geneva School of Economics and Management, University of Geneva 95.04, Institut d'Economie et Econométrie, Université de Genève.
  2. Chris Shannon & William R. Zame, 2000. "Quadratic Concavity and Determinacy of Equilibrium," GE, Growth, Math methods 9912001, EconWPA.
  3. Covarrubias Enrique, 2010. "Regular Infinite Economies," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-21, July.
  4. Enrique Covarrubias, 2010. "The Equilibrium Set of Economies with a Continuous Consumption Space," Working Papers 2010-10, Banco de México.
  5. Timothy J. Kehoe & David K. Levine, 1982. "Comparitive Statics and Perfect Foresight in Infinite Horizon Economies," UCLA Economics Working Papers 259, UCLA Department of Economics.
  6. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
  7. Balasko, Yves, 1997. "Pareto optima, welfare weights, and smooth equilibrium analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 21(2-3), pages 473-503.
  8. Accinelli, Elvio, 2013. "The equilibrium set of infinite dimensional Walrasian economies and the natural projection," Journal of Mathematical Economics, Elsevier, vol. 49(6), pages 435-440.
  9. Balasko, Yves, 1997. "The natural projection approach to the infinite-horizon model," Journal of Mathematical Economics, Elsevier, vol. 27(3), pages 251-263, April.
  10. Elvio Accinelli, 2003. "About manifolds and determinacy in general equilibrium theory," Estudios de Economia, University of Chile, Department of Economics, vol. 30(2 Year 20), pages 169-177, December.
  11. Elvio ACCINELLI & Puchet MARTIN, . "A Classification Of Infinity Dimensional Walrasian Economies," EcoMod2005 280900000, EcoMod.
  12. Chichilnisky, Graciela & Zhou, Yuqing, 1998. "Smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 29(1), pages 27-42, January.
  13. Timothy J. Kehoe & David K. Levine & Andreu Mas-Colell & William Zame, 1989. "Determinacy of Equilibrium in Large Square Economies," Levine's Working Paper Archive 46, David K. Levine.
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